A number of four different digits is formed with the help of the digits 1,2,3,4,5,6,7 in all possible ways. How many such numbers can be formed?

Explanation

Here total digit-7 and no two of which are alike
(i) Required number of ways=Taking 4 out of 7
`=.^(7)P_(4)=7xx6xx5xx4=840`
(ii) For even number of last digit must be 2 or 4 or 6. Now the remaining three first places on the left of 4-digit numbers are to be filled from the remaining 6-digits and this can be done in
`.^(6)P_(3)=6*5*4=120` ways
and last digit can be filled in 3 ways.
`therefore`by the principal of multiplication, the required number of ways
`=120xx3=360`